Answer the Following:

Question

a.) In the figure, which angles are exterior angles of a triangle?

b.) What is the relationship of measure angle DAC to measure angle B? Why?

c.) What is the relationship of angle DAC to angle BAE? Why?

d.) What is the relationship of angle DAC to angle BAC? Why?

Answer 1

a) Angles DAC and BAE are exterior angles.

b) There is theorem that states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles; that is m∠DAC = m∠B + m∠C

c) Angles DAC and BAE are vertical angles, and have the same measure.

d) Angles DAC and BAC are supplementary angles (their measures sum to 180°)

Answer 2

Exterior angles are angles formed outside the triangle that are adjacent to an angle inside the triangle:

a) <DAE and <BAE are exterior angles

b) <DAC is an exterior angle to angle <B because <B is an interior angle non-adjacent to <DAC

c) <DAC and <BAE are vertical angles because they are opposite angles formed by the intersection of two lines

d) <DAC and <BAC are linear pair because they are adjacent angles formed by the intersection of two lines.